#Greeshma Ganji
# Splitting the data set into a training set and a test set.
library(ISLR)
library(tree)
library(randomForest)
## randomForest 4.7-1.1
## Type rfNews() to see new features/changes/bug fixes.
set.seed(1)
train <- sample(1:nrow(Carseats), nrow(Carseats) / 2)
Carseats.train <- Carseats[train, ]
Carseats.test <- Carseats[-train, ]
# Fitting a regression tree to the training set and plotting the tree to interpret the results.
tree.carseats <- tree(Sales ~ ., data = Carseats.train)
summary(tree.carseats)
##
## Regression tree:
## tree(formula = Sales ~ ., data = Carseats.train)
## Variables actually used in tree construction:
## [1] "ShelveLoc" "Price" "Age" "Advertising" "CompPrice"
## [6] "US"
## Number of terminal nodes: 18
## Residual mean deviance: 2.167 = 394.3 / 182
## Distribution of residuals:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -3.88200 -0.88200 -0.08712 0.00000 0.89590 4.09900
plot(tree.carseats)
text(tree.carseats, pretty = 0)
yhat <- predict(tree.carseats, newdata = Carseats.test)
mean((yhat - Carseats.test$Sales)^2)
## [1] 4.922039
# the Test MSE is about 4.92
# Using cross-validation to determine the optimal level of tree complexity.
cv.carseats <- cv.tree(tree.carseats)
plot(cv.carseats$size, cv.carseats$dev, type = "b")
tree.min <- which.min(cv.carseats$dev)
points(tree.min, cv.carseats$dev[tree.min], col = "red", cex = 2, pch = 20)
# Pruning the 14-node tree to obtain best results.
prune.carseats <- prune.tree(tree.carseats, best = 14)
plot(prune.carseats)
text(prune.carseats, pretty = 0)
yhat <- predict(prune.carseats, newdata = Carseats.test)
mean((yhat - Carseats.test$Sales)^2)
## [1] 5.013738
# It can be observed that pruning the tree increases the Test MSE to 5.01
# Using the bagging approach in order to analyze this data
bag.carseats <- randomForest(Sales ~ ., data = Carseats.train, mtry = 10, ntree = 500, importance = TRUE)
yhat.bag <- predict(bag.carseats, newdata = Carseats.test)
mean((yhat.bag - Carseats.test$Sales)^2)
## [1] 2.657296
# bagging decreased the Test MSE to 2.65
importance(bag.carseats)
## %IncMSE IncNodePurity
## CompPrice 23.07909904 171.185734
## Income 2.82081527 94.079825
## Advertising 11.43295625 99.098941
## Population -3.92119532 59.818905
## Price 54.24314632 505.887016
## ShelveLoc 46.26912996 361.962753
## Age 14.24992212 159.740422
## Education -0.07662320 46.738585
## Urban 0.08530119 8.453749
## US 4.34349223 15.157608
#Price and ShelveLoc are the two most important variables.
rfNews()
# Using random forests to analyze this data.
rf.carseats <- randomForest(Sales ~ ., data = Carseats.train, mtry = 3, ntree = 500, importance = TRUE)
yhat.rf <- predict(rf.carseats, newdata = Carseats.test)
mean((yhat.rf - Carseats.test$Sales)^2)
## [1] 3.049406
# The Test MSE is 3.3
importance(rf.carseats)
## %IncMSE IncNodePurity
## CompPrice 12.9489323 158.48521
## Income 2.2754686 129.59400
## Advertising 8.9977589 111.94374
## Population -2.2513981 102.84599
## Price 33.4226950 391.60804
## ShelveLoc 34.0233545 290.56502
## Age 12.2185108 171.83302
## Education 0.2592124 71.65413
## Urban 1.1382113 14.76798
## US 4.1925335 33.75554
#Price and ShelveLoc are the two most important variables.